基于有限样本的可行广义最小二乘法

本文在Choi,Hu和Ogaki（2008）的基础上,研究样本量有限时,可行广义最小二乘（FGLS）法在解决虚假回归问题时的表现。通过蒙特卡罗模拟实验,发现FGLS方法可以有效消除单位根序列及平稳自相关序列间的虚假回归现象,但在单位根序列长度较小时,表现不佳。进一步对FGLS估计值及统计检验值进行理论计算和分析,说明单位根序列长度较小时,虚假回归现象不能被有效消除的必然性,且在采用FGLS方法修正单位根序列间的虚假回归问题时,估计式中常数项是无意义的。此外,本文还以研究沪、深股市指数间关联关系为例,对差分普通最小二乘（DOLS）回归法和FGLS两种建模方法进行比较,结果表明当样本量足够大时,在动态预测精度的评价标准下,FGLS方法更好。     

面向售后服务的汽车备品需求预测研究

根据面向售后服务的汽车备品需求特点的差异,本文将其分为专用配件和通用配件并分别选用不同的预测模型.对专用配件,采用基于时间序列相关的线性回归模型,并运用加权最小二乘法（WLS）估计参数.对通用配件,选用GM（1,1）模型进行需求预测.     

成分数据偏最小二乘 Logistic回归模型及其应用

成分数据由于存在定和约束和多重共线性，在进行传统的logistic回归建模时遇到了困难。本文在对称logratio变换和偏最小二乘logistic回归技术的基础上，提出了成分数据偏最小二乘logistic回归模型，较好地解决了成分数据的logistic回归建模问题。应用此方法，本文研究了中国三次产业就业结构与人民生活水平之间的关系。结果表明，该模型在有关结构问题的logistic回归建模中具有很好的适用性。     

联立方程模型的工具变量方法质疑与商榷

本文质疑联立方程模型前定变量的工具变量性质：前定变量并不保证与当期行为解释变量的相关性,由其构建的工作回归元所完成的分阶段最小二乘估计因而并非两阶段最小二乘估计。建议按照简约式方程构建工作回归元,其具有模型数理逻辑支持下的可替代意义。工作回归元的不同导致结构式方程分阶段最小二乘估计的不同结果,之于恰好识别方程则揭示了业内关于间接最小二乘估计方法的一个误区。     

基于自相关的自回归模型参数的折扣最小二乘估计

本文简要介绍了基于自相关的自回归模型参数的折扣最小二乘估计。     

考虑结构突变时确定性趋势的估计与单位根检验式的选择——基于可行广义最小二乘估计的分析

单位根的检验功效依赖于回归检验式中的确定性趋势,而趋势估计量的分布又取决于序列的平稳性,两者相互制约。鉴于此,本文借鉴了Perron和Yabu(2009)提出的可行广义最小二乘估计,推导了相关统计量的分布,在考虑结构突变的情况下,构造了一套确定性趋势的估计和推断程序,并通过蒙特卡罗模拟对该程序的有限样本性质进行了分析。结论显示,大多数情形下根据该程序进行的单位根检验具有较高功效。     

具有异质性非参数时间趋势的面板数据模型的估计

本文为一类具有异质性非参数时间趋势的面板数据模型提出了一种简单估计方法。基于局部多项式回归的思想,首先去除数据中的时间趋势成分,然后由最小二乘法来估计公共系数,同时得到时间趋势函数的非参数估计。在一些正则条件下,研究了这些估计量的渐近性质,即在时间维度T和横截面维度n同时趋向无穷时,建立了各个估计量的渐近相合性和渐近正态性。最后通过蒙特卡洛模拟,考查了这种估计方法的有限样本性质。     

基于偏最小二乘的泰国菠萝出口影响因素实证研究

本文采用偏最小二乘回归模型(PLS),以泰国菠萝贸易为例,通过变量投影重要性准则筛选自变量,由交叉有效性提取主成分,进而建立偏最小二乘回归模型。深入分析了各指标对泰国菠萝出口贸易的影响。研究表明泰国菠萝出口与原料价格及工厂生产加工速度密切相关,并且偏最小二乘回归的拟合效果优于普通最小二乘回归。     

基于结构突变和截面相关的面板协整检验

本文基于Westerlund和Edgerton（2008）,考虑了无时间趋势和有时间趋势的面板协整检验。在检验协整时,本文不仅允许误差项存在异方差、序列相关以及截面相关,而且还允许各截面在截距和协整斜率上存在未知时点的多个突变点。蒙特卡洛模拟结果表明,（1）该检验的具有较小的水平扭曲和较高的检验势,（2）将模型拓展到不含有趋势项的情形是必要的。在此基础上,使用基于动态最小二乘估计量的新统计量对国际CO2排放和经济增长关系进行检验,发现在考虑了突变和截面相关的情形下,两者间的长期均衡关系确实存在。     

存在遗漏变量时的内生性研究

存在遗漏变量时回归系数的估计是计量经济学的一个重要内容。本文讨论单方程计量经济模型中随机解释变量的内生性,指出了目前的计量经济理论所存在的问题,提出了普通最小二乘估计一致性判别的新方法,并证明了存在遗漏变量情况下的普通最小二乘估计仍是一致估计。     

Is Stock Price Correlated with Oil Price? Spurious Regressions with Moderately Explosive Processes

This study explores the spurious effects in linear regressions with moderately explosive processes. Asymptotic results are developed for the least square estimator, the typical t‐statistic, the Durbin–Watson statistic, and the coefficient of determination. The typical t‐statistic is unable to detect the presence of a spurious relationship, due to the presence of nuisance parameters that characterize deviations from unity. Moreover, the t‐statistic for common explosive processes has different asymptotics compared to that for distinct explosive processes. Such differences further complicate the use of the t‐statistic. We demonstrate that two popular methods available in the literature are incapable for this purpose due to similar difficulties. To overcome these limitations, we propose a t‐test based upon balanced regressions that induces asymptotic inference based on the standard normal distribution, which is therefore robust to deviations from unity. These results are further generalized to spurious regressions with multivariate mildly explosive processes. Simulation results confirm that our test is effective in finite samples, while other alternatives are not. An empirical example that demonstrates the phenomenon of spurious correlation between the NASDAQ stock index and crude oil price in the US is provided to show the practical merit of our proposed method.     

Robust estimation for structural spurious regressions and a Hausman-type cointegration test

This paper analyzes an approach to correcting spurious regressions involving unit-root nonstationary variables by generalized least squares (GLS) using asymptotic theory. This analysis leads to a new robust estimator and a new test for dynamic regressions. The robust estimator is consistent for structural parameters not just when the regression error is stationary but also when it is unit-root nonstationary under certain conditions. We also develop a Hausman-type test for the null hypothesis of cointegration for dynamic ordinary least squares (OLS) estimation. We demonstrate our estimation and testing methods in three applications: (i) long-run money demand in the U.S., (ii) output convergence among industrial and developing countries, and (iii) purchasing power parity (PPP) for traded and non-traded goods.     

A control function approach for testing the usefulness of trending variables in forecast models and linear regression

Many predictors employed in forecasting macroeconomic and finance variables display a great deal of persistence. Tests for determining the usefulness of these predictors are typically oversized, overstating their importance. Similarly, hypothesis tests on cointegrating vectors will typically be oversized if there is not an exact unit root. This paper uses a control variable approach where adding stationary covariates with certain properties to the model can result in asymptotic normal inference for prediction regressions and cointegration vector estimates in the presence of possibly non-unit root trending covariates. The properties required for this result are derived and discussed.     

Spurious relationships in high-dimensional systems with strong or mild persistence

This paper is concerned with the interactions of persistence and dimensionality in the context of the eigenvalue estimation problem of large covariance matrices arising in cointegration and principal component analysis. Following a review of the early and more recent developments in this area, we investigate the behaviour of these eigenvalues in a vector autoregression setting that blends pure unit root, local to unit root and mildly integrated components. Our results highlight the seriousness of spurious relationships that may arise in such big data environments even when the degree of persistence of the variables involved is mild and affects only a small proportion of a large data matrix, with important implications for forecasts based on principal component regressions and related methods. We argue that, prior to principal component analysis, first-differencing may be suitable even in stationary or nearly stationary environments.     

Trending time-varying coefficient time series models with serially correlated errors

This paper studies a time-varying coefficient time series model with a time trend function and serially correlated errors to characterize the nonlinearity, nonstationarity, and trending phenomenon. A local linear approach is developed to estimate the time trend and coefficient functions. The asymptotic properties of the proposed estimators, coupled with their comparisons with other methods, are established under the α$\alpha$-mixing conditions and without specifying the error distribution. Further, the asymptotic behaviors of the estimators at the boundaries are examined. The practical problem of implementation is also addressed. In particular, a simple nonparametric version of a bootstrap test is adapted for testing misspecification and stationarity, together with a data-driven method for selecting the bandwidth and a consistent estimate of the standard errors. Finally, results of two Monte Carlo experiments are presented to examine the finite sample performances of the proposed procedures and an empirical example is discussed.     

A semi-parametric Bayesian approach to the instrumental variable problem

We develop a Bayesian semi-parametric approach to the instrumental variable problem. We assume linear structural and reduced form equations, but model the error distributions non-parametrically. A Dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors. Our implementation of the Dirichlet process prior uses a normal distribution as a base model. It can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components. We demonstrate that this procedure is both feasible and sensible using actual and simulated data. Sampling experiments compare inferences from the non-parametric Bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics. When errors are non-normal, our procedure is more efficient than standard Bayesian or classical methods.     

Density Forecasts With Midas Models

We propose a parametric block wild bootstrap approach to compute density forecasts for various types of mixed‐data sampling (MIDAS) regressions. First, Monte Carlo simulations show that predictive densities for the various MIDAS models derived from the block wild bootstrap approach are more accurate in terms of coverage rates than predictive densities derived from either a residual‐based bootstrap approach or by drawing errors from a normal distribution. This result holds whether the data‐generating errors are normally independently distributed, serially correlated, heteroskedastic or a mixture of normal distributions. Second, we evaluate density forecasts for quarterly US real output growth in an empirical exercise, exploiting information from typical monthly and weekly series. We show that the block wild bootstrapping approach, applied to the various MIDAS regressions, produces predictive densities for US real output growth that are well calibrated. Moreover, relative accuracy, measured in terms of the logarithmic score, improves for the various MIDAS specifications as more information becomes available. Copyright © 2016 John Wiley & Sons, Ltd.     

Spurious Regression and Trending Variables*

This paper analyses the asymptotic and finite‐sample implications of different types of non‐stationary behaviour among the dependent and explanatory variables in a linear spurious regression model. We study cases when the non‐stationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t‐statistic in a spurious regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases when both dependent and explanatory variables behave in a non‐stationary way. Simulation experiments confirm our asymptotic results.     

On the Geometry of the Instrumental Variable Estimator*

I derive the exact distribution of the exact determined instrumental variable estimator using a geometric approach. The approach provides a decomposition of the exact estimator. The results show that by geometric reasoning one may efficiently derive the distribution of the estimation error. The often striking non‐normal shape of the instrumental variable estimator, in the case of weak instruments and small samples, follows intuitively by the geometry of the problem. The method allows for intuitive interpretations of how the shape of the distribution is determined by instrument quality and endogeneity. The approach can also be used when deriving the exact distribution of any ratio of stochastic variables.     

Reliable inference for the Gini index

Although attention has been given to obtaining reliable standard errors for the plug-in estimator of the Gini index, all standard errors suggested until now are either complicated or quite unreliable. An approximation is derived for the estimator by which it is expressed as a sum of IID random variables. This approximation allows us to develop a reliable standard error that is simple to compute. A simple but effective bias correction is also derived. The quality of inference based on the approximation is checked in a number of simulation experiments, and is found to be very good unless the tail of the underlying distribution is heavy. Bootstrap methods are presented which alleviate this problem except in cases in which the variance is very large or fails to exist. Similar methods can be used to find reliable standard errors of other indices which are not simply linear functionals of the distribution function, such as Sen’s poverty index and its modification known as the Sen–Shorrocks–Thon index.